The Rest Is Science - The Device That Maps The Heavens

Episode Date: December 18, 2025

Tucked away in old engineering kits and museum drawers is a device whose sweeping motion once captivated mathematicians and designers alike.  The ellipsograph: a mechanical tool built from sliding arms and rotating joints that were tracing flawless curves long before computers made such things effortless. While they have the appearance of an ancient curiosity, the ellipsograph’s power lies in its ability to transform abstract geometry into tangible motion on a page. Its careful movement can physically enacts the strict mathematical conditions that define an ellipsis - a shape that’s central to geometry, but also to the natural order of the cosmos. So is this object just a relic of the past? Or does it have a place in the present? As a reminder of the deceptive simplicity that rules the world around us, and the ingenuity required to understand it. Welcome to The Rest Is Science: Field Notes. Each Thursday, Hannah and Michael rummage through their personal troves of scientific treasure to source objects that expand our understanding the universe, that scramble our brains, that hint at forces we’ll never see...and, that are sometimes, just plain old cool. Expect deep dives into the science behind each pick, the spark that grabbed their attentions, and the sheer delight they get from sharing it all with you. They’ll also be tackling your questions, so email The Rest Is Science at [e-mail]. ------------------- For more information about Cancer Research UK, their research, breakthroughs and how you can support them, visit ⁠⁠https://cancerresearchuk.org/restisscience⁠⁠ Cancer Research UK is a registered charity in England and Wales (1089464), Scotland (SC041666), the Isle of Man (1103) and Jersey (247). A company limited by guarantee. Registered company in England and Wales (4325234) and the Isle of Man (5713F). Registered address: 2 Redman Place, London, E20 1JQ. ------------------- Find The Rest Is Science all over the internet by ⁠clicking here.⁠ ------------------- Video Producer: Oli Oakley Video & Social: Bex Tyrrell Assistant Producer: Imee Marriott Producer: Becki Hills Senior Producer: Lauren Armstrong-Carter Head Of Digital: Samuel Oakley Exec Producer: Neil Fearn Learn more about your ad choices. Visit podcastchoices.com/adchoices

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Hello and welcome to The Rest is Science. Today is an episode of Field Notes where Hannah and I share amazing stories, objects, our deepest fears. Oh, we're going there today, oh. We might be, or we might not. If you have questions or things you want to share with us,

you can always reach out. We would love to take on those. But today, Hannah told us, me that she brought something related to ellipses. I did. Okay. If you want to draw a circle, easy, easy, get a compass. Hold on.

I want to guess what you brought. You've already given me a piece of information that's almost confirming what I was going to guess. Oh, really? Okay. Let's imagine I did. Okay. Is it an ellipsograph? It might be.

Is it just an ellipsograph? Does it allow me to draw an ellipse? Or does it simply trace an ellipse in a surprising way? It allows you to draw. raw one, but I think in a surprising one, I think in a very beautiful way. Is it a circle that rolls on the inside of another circle? No. Okay.

Let's see it. Okay, you want to draw a circle. You get the compass from your primary school pencil case that you have not opened since and never needed to use in actual real life. And that's fine because you just, a circle is a fixed distance from a single point and trace out the arc, right? Easy. piece. Elips is way harder.

Way harder. Because instead of having one focus, you have two. And you can do it by putting two pins into a piece of paper and like tying a single piece of string between the two and then using a pencil to kind of trace out that arc. That is one way of doing it. So,

some friends of mine at Maker's Cabinet have over-engineered a way to draw ellipses. And I thought you might enjoy it. Yeah. You know, you're sort of like a draftsman in you somewhere. Yeah, there is. The key point here is that an ellipse is a fixed distance between two foci, okay, between two points. So what does that mean?

That means that no matter where you are on the ellipse, the combined distance from that point to both foci is fixed. Is the same. Exactly right. Got it. Okay. So do you want to have a little play with this? Yeah. I can get out to work. Okay.

Okay. So there's a magnet. Oh, that's a nice strong magnet. There's a magnet underneath this page. This sits on it Ah yeah I wanted people to appreciate this ellipsograph Look at this

Those shuttles are following Straight Line tracks And yet We trace out an ellipse From circular motion Well from linear motion We get circular motion I love that

It's so well made It's beautiful isn't it I've seen them made of wood and plastic But this is like brass Look at that Isn't that beautiful What a treat. I mean, isn't that a treat?

Yeah. They're the coolest objects. They're how the planets move. They are how the planets move. But the thing is that there was such big arguments about the idea that that is how the planets move. Because the Greeks in particular were obsessed with circles. They thought there was like the platonic ideal, the symmetry of it, the beauty of it, it's just absolute perfection. And this stood for a really long time, this idea of circles.

I mean, like thousands and thousands of years, people thought it's circles that's going on. in the sky. And then Tico bra, or sometimes people say Tyco, don't they? I say Tyco. I say Tyco, bra. From now on that is how are we known? And he was a bit of a bra, actually. He got into an argument with someone about a formula, had a jewel, ended up losing his nose. No kidding. You know this, right? I didn't know this. So he lost his nose, so he had a prosthetic nose. He had different ones. He had a bronze one. He had a silver one for special occasions. And then a gold one.

that flickered in the candlelight to look realistic. But he collected all of these observations of celestial objects in the sky. He also had a pet elk that he used to like bring around to places. In the end, the elk passed away because it got drunk. Oh, no. Got the elk drunk and tried to take it downstairs. Anyway, whatever. He was a bit of a dude, yeah.

This was in like the late 1500s. Exactly, exactly, early 1600s, exactly. and he collected all of these observations and he handed off all of that data to his assistant Kepler and Kepler was like looking for the circles looking for the circles

trying this circle that circle and then eventually came to the conclusion that no it's not circles, it's ellipses and he said that it was like a cartload of dung that he had to swallow because he just hated

hated the idea that there might be anything other than circles in the sky But it was. But it was. And swallowing that heap of dung really moved us forward. It really did. Imagine that.

Being like, oh, here's my assistant, Kepler. Like, can you imagine better help? Speaking of the motion of planets, that's perfect because I actually brought something related to them. Now, this shows them in circular orbits. Sorry, Kepler, but it's a simplified thing for a reason. Watch. This is an aurary calendar. It's a page a day calendar.

It doesn't tell you an inspirational quote for each day or give you a Sudoku for each day. It shows you the relative positions of the planets each day. So this is January 1st of 2026. It's a 2026 calendar. And then the next one is... We actually got two of January 1st. And then the next one is Friday, January 2nd. And as you can see...

Almost imperceptible. It almost don't change. However, you use it like a flip. book and you can see just how quickly the planets are moving in their orbits. Okay, sure, show, show, sure, sure, sure. So Neptune basically doesn't move at all in a year, but Earth goes all the way around once. Okay. Now, full disclosure, you can only flip it backwards easily.

You kind of have to like break the back. Oh, that is amazing. So you can plan ahead and be like, oh, I want to do that thing, but only when Uranus is as far away from Earth as it's going to be all year. And they've got the moon phases on them. It sort of feels like more than 360 pages, but it isn't. Well, we made it out of a special recyclable paper, like a compostable paper, because I was like, if we're going to print this many sheets, I want to keep Earth happy. That is absolutely delightful.

Mercury whizzing around there. I know, isn't it nuts? And Jupiter just barely, I mean, it's taking its time. Jupiter takes its time to go around the sun, but around its own axis, Jupiter is like really fast. It takes the Earth 24 hours to go once around its axis, but it takes Jupiter just, 10 hours. So it's two and a bit days for every day? That's wild because Jupiter is huge.

Yeah. So if you are some gas out on the edge of Jupiter around the equator, you are booking it. Like, no wonder that great red spot won't go away. The storms on Jupiter have an enormous amount of energy just from that planet whipping it around. I'm just liking the idea of being on a spaceship and just your face being pulled back with the speed of it.

Well, I mean, it's not quite that fast. I mean, none of us are on Earth. Earth being like, whoa, even though we are rotating at, you know, hundreds of miles per hour around its axis, Earth is just too big even for us to appreciate that. Don't ruin my memory. It does make us a little bit lighter in the same way that when you're on a spinning carnival ride, you feel like you're being pulled away. Really, you're being pulled tangential to the circle.

But on Earth, we are feeling that motion too. And so we weigh a few fractions of a gram less because of its rotation. And if it stopped moving, we'd be like, oh, all of the gravity. I'm feeling all of it. So wait, what's that on Jupiter then? So you're spinning faster, but it is heavier? You're spinning faster. So you've got an even greater, like, uplift.

We often call it a centrifugal force when it's not really a force, but it's that like, whoa, I'm moving away from the center of rotation of my curve. When in reality, you're leaving tangential to the path. But on a big circle, that feels like going straight up. There's a ride at Thought Park. And what's interesting about it is that it has the longest negative G, basically. So you are effectively airborne, if you like, in your seat. But the way that they have to do it, you know, normally you are, as you go on a roller coaster,

you are forced into your seat, right? So you're going to go down. It's like you're like, whoa, like really feel the weight of it. In this one, it's the opposite. And the way that they do it is they have to slow down the carriage as it, goes on the outside of a turn in order for you to really have that that feeling sort of being flung out into the air. Whoa.

I won't be writing on that anytime soon. I don't, no. I just, I never had. As a kid, I actually collected newspaper clippings of deaths on roller coasters. Because it made me feel like my fear was justified. I still have the box. It's actually the box that my Bill Nye fan club subscription goodies came in and then I just put little comics and recipes and

deaths at the Worlds of Fun theme park in Kansas City all in there. Please one day can we do a field note where you go through that box? Yeah, we sure can. It's going to be a lot of like corny family circus cartoons that I thought were quite clever when I was eight.

But I brought one more thing. This is actually for your two daughters. Okay, amazing. You better believe I'm stealing this, by the way, just to be absolutely clear. You cannot steal that because I have to make a video about it and it's the only one I have.

I will get you one that can be just yours. Here's two CMY cubes. These are the additions that we put in a curiosity box, as if I'm going to buy anything for you. But the couple who invented those are fantastic people, and we partnered with them to make this addition of their CMY cube. It is a translucent cube, about two inches on each edge. and opposite faces of the cube have the same color, the same translucent color. And the colors that you'll find are, there's three of them,

cyan, magenta, and yellow, CMI. Those are primary colors in the CMI system, and you can combine them to make all kinds of other colors. You've got magenta, then twist it, you've got yellow, and then twist it again, and you have got cyan. Cyan. I mean, is the colors you get in your printer. That's right.

But if you combine them together, hang on. Does it work? Does it work? It does work. Yeah. I'm just trying to work it out what the colors would do. It can be very confusing because there's not just the subtractive color mixing that's

happening. There's also reflection, but greens and purples and oranges are produced as the light is subtractively changed. Passing through the cyan filter. only cyan comes through. Hey, do you know where you send naughty rainbows? Where? To prism.

I do like that prisms can create rainbows, but they can also destroy them. If you send a prism through a rainbow, it comes out as white light. Does it? Yeah. And if you look at a rainbow, like a rainbow in a children's book through a prism, at the right distance, it'll get smashed into just a white line. Yeah. These are absolutely amazing.

They're really beautiful. Really beautiful. And they're really well made. Also, what I notice is like the sorts of truth. This is the second object that you've given me for my children with extremely sharp edges. Oh, that's right. Yeah. You're welcome. Amazing. Should you go to a break? Let's take a break. This episode is brought to you by Cancer Research UK.

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The first stage of the trial starts this year, focusing on people at higher risk. It shows what long-term research makes possible. For more information about Cancer Research UK, their research breakthroughs and how you can support them, visit cancerresearchuk.org forward slash the rest is science. Amazon presents Jeff versus Taco Truck Salsa, whether it's Verde, Roja, or the Orange one. For Jeff, trying any salsa is like playing Russian roulette with a flamethrower. Luckily, Jeff saved with Amazon and stocked up on antacids, ginger tea, and milk. Habaniero, more like habanier, yes. Save the everyday with Amazon.

This episode is brought to you by Defender. With its 626 horsepower twin-turbo V8 engine, the Defender Octa is taking on the car rally, the ultimate off-road challenge. Learn more at landrover.ca. Welcome back. This is field notes. An extra half an hour that you get to spend in the company of me and Michael every single week where we try and impress each other with things that we know, things that we found. I'm not trying to impress you with any of this. Oh, I'm absolutely trying to impress you. I'm trying to impress my mom. Yeah, aren't we all? Aren't we all? Anyway, sorry, this got really deep. Deep very quickly. Let's lighten it up.

Who's got a question? Should we go to the mailbag? Yeah. Okay. All right, we've got some interesting questions this week. By the way, please do feel free to send in your questions to the rest of science at goalhanger.com. All right. Alana asks, you can invite three other people from the world of science who are dead or alive to a dinner party who you choose in.

Oh, my gosh. Do you have an answer? I mean, I've definitely got some favorites. Yeah, sure, sure, sure. I feel like, you know, Albert Einstein is one of the more obvious cliche types of answers, but I want to know what his last words were. You know, he spoke them in German to a nurse who did not know German. And so they've been lost. No.

I want to know if it was like, oh, crap. Or if it was like, oh, it's actually MCC, you know, or something. I don't know. But I would love to find out. I'd also like to know how he feels about it. You know the story about Einstein's brain? Oh, his brain? Yes.

And then it was sort of extracted, put in a jar, and then just forgotten about. That's right. It was in the back of a cupboard and someone found it years later and were like, what is this? And it turned out to be Einstein's brain. And this was at like a medical facility, by the way. It wasn't just like, oh, his neighbors came over and pulled it out. It was like donated to be studied and then just forgotten about. In a little medical closet.

But when they did study it, they basically found there was nothing remarkable about it, right? Maybe slightly more white matter than the rest of us. Okay. I'd like to ask him about that. I would like to ask him about that. How do you feel about your brain being forgotten about in a cupboard for a very long time? Yeah.

Okay, so besides Einstein, who's on your list? Okay, I would quite like to meet Galois. Who is that? Okay, so Galois is like he's such a dude. He's this French mathematician. He's like 19, 20 years old. And he is super. super, super, super bright, but he's also

very French and loves to have affairs with beautiful women. One of the people he has an affair with turns out to be engaged to some very important soldier in the town who challenges him to a duel and of course

because he is very French and this is around 1700s, you can't turn down a duel. So he agrees to go off and have the jewel, have the fight with this, you know, with his lover's partner. With four he does that. He decides he needs to finish his math theory. Okay. So he stays up all night and he scribbles this stuff down. It's all about, you know, you have quadratics, which is where you have,

where you have something squared. Yeah. You have cubics, which is, which is cubed to the power of three. But he was looking at quartics and quintix. Wow. Equations to the power five, right? I'll be honest, it gets very hard, very quickly. Yeah. But so he's there. He's like, I've got to, I've got to work out these equations, I've got to work out these equations. And we still have the kind of ink splattered pages that he wrote on that night. Every now and then he's like, he's scribbling down the theory, he's crossing stuff out and then he writes like, La femme, la femme. And then he's like, oh, I'm going to die in the morning.

It's like, no, I've got to go back to these equations. Anyway, he goes off, he does the jewel, he loses in the jewel, he loses his life. But those pages and the work that he did in advance of that then goes on to be absolutely foundational and now every person who goes to studying mathematics as a degree level will learn Galois theory. This 20 year old kid. What a romantic story that is. Wow.

It's like if he'd been given just a couple more days, what else could he have discovered? Or was it the impending possibility of death that made him work so well? It just spilled off all that brilliance at once. I'd just like to meet him at dinner and be like, you idiot. You idiot. That would be very cool. Can we go to the same dinner party together? Okay.

So we've got Einstein and Galois. We could go way back in time. Like I'm thinking about a Pythagoras would be neat. This is sort of the world of math at this point. But like, I want to hear about the meaning of numbers to him. What do they mean to you? It was much more religious. He didn't really like numbers.

I mean, they didn't really like numbers at all, the Greeks. Not all of them. Sure. Those irrational ones. Those irrational ones, they weren't so happy with. They were like the demons. obviously Archimedes. I think it'd be cool just to say that I met him.

I love that of all the things Archimedes did, the inventions, the Eureka, I'm in a bathtub, and I've learned about volume and how to measure it. The story goes that on his gravestone, do you know what he had them put there? Go on. A sphere, a cylinder, and a cone of equal heights. Because he showed the relationships between their volumes. And he was so proud of that that he was like, Like of everything I did, I want that to be what's on my grave.

His alchemyed is the one who died at the hand of a soldier who was trying to capture him. I think there was some sort of invasion of his island. And then he was told to, because he was such a genius, they were like going to capture him and bring him back to the whatever king. Okay. Something. The soldier went in and was like, you need to come with me. And he was like, don't disturb me when I'm with my circles.

And so the soldier killed him. Wow. Yeah. For the circles. For the circles. You just couldn't give them up. Yeah. Maybe instead of doing like, maybe instead of picking people based on the interesting things they have to offer, maybe we just get the people who've got the most stupid deaths in science.

Yeah, right. And we can just make fun of them. Just make fun of them. You could bring Archimedes and then have a bunch of circle foods, okay? Yeah. Slices of bologna, pie pizzas. Yeah. And be like, hey, let's cut them up.

Let's make some cords, some diameters. In your honor. In your honor. Here is this, here's a cone-shaped cake. So, yeah, it's not so much to learn from them, but it's to honor them and kind of razz him a bit. Yeah, I'd be up for that. That sounds like a good dinner party. Actually, Pythagoras himself, he's got an amazing death.

Do you know about Pythagoras's death? No. Okay, so, I mean, this is possibly apocryphal, but I'll be honest with you. A lot of stories that old are. Sure. Yeah. Right. Pythagoras of Triangle fame, absolutely amazing. We had a school, basically, like, had loads of, you know, disciples.

terrified of beans, really, really hated them, thought that they looked like sort of miniature humans, just really, he absolutely appalled them. Yeah, who hasn't thought that? What? Who hasn't thought that? Beans were banned in his school. Okay, got it.

And the rumor goes that he had sort of a fight with some other people, they wanted to join a school, he didn't let them, they barricaded his house, set it on fire, and he ran away, managed to get free, ran away, and they were chasing him, and then he carried him running, and it was all fine until he came up, to a field of beans

and he refused to run through the field of beans as they caught up with him and killed him. Wow. This sounds like a great dinner party. Beans and pizza for dinner. Would you bring beans? Yeah.

Would you not bring beans? Bean pizza. Bean cookies. Like a can of refried beans is a cylinder. Archimedes would love that Pythagoras wouldn't but you know he's got a lot of credit.

It's time for him to get a little roasting. Roasting. That's right, that's right. Well, we've got one more question. This one is from Fred. Fred asks, why do Goldfish have such short memories? Okay, I think that this is a massive misconception.

I was wondering if that might be, yeah. I think that actually there have been experiments with goldfish where they can sort of be shown to navigate a maze to get food and then can remember the route that they've learned months afterwards. So where did this misconception start? I think it's just snobbery. Right. It's just straight up snobbery. But also, it really does, I think, underline the cruelty of putting a goldfish in a bowl where it's got nothing to do. Because, of course, if it's only got a three second memory, who cares that it doesn't have anything to interact with?

But, I mean, we did an episode about boredom. All this time, those pretty little goldfish that we've been having to effectively decorate our homes. We've been essentially torturing them. Yeah, I don't know what kind of space they need. But, yeah, a three second memory seems. pretty made up. Maybe to make us feel better about like, oh, yeah, there's not much to do there. But yeah, I don't know how much room they need. They might even need, like, a place where they feel like they can go to be safe and hidden, like a little, you know, rock cave feature.

Maybe a goldfish friend. A goldfish friend. Yeah. Do they like having friends? I wouldn't be surprised they did. Yeah. Yeah. I've never owned one of you. I might have had one when I was, like, four. Because I kind of remember fish, but not since then. My daughter really wants a bird. Oh yeah. And I'm like, birds deserve to be free. Not going to happen.

So I had a cockatiel when I was younger. What was interesting about him is he would sit on your shoulder in the garden. Oh, outdoors. Yeah. And not leave. And not leave. I think you can bond with the bird. I think that's my point.

I think you can bond with the bird. I believe that for sure, for sure. And you guys can bond with us by joining our newsletter at the rest is science at goalhanger.com.